Estimating the spectrum of a density operator

Given N quantum systems prepared according to the same density operator rho. we propose a measurement on the N-fold system that approximately yields the spectrum of rho. The projections of the proposed observable decompose the Hilbert space according to the irreducible representations of the permutations on N points. and are labeled by Young frames, whose relative row lengths estimate the eigenvalues of rho in decreasing order. We show convergence of these estimates in the limit N --> proportional to, and that the probability for errors decreases exponentially with a rate we compute explicitly.